Rational Points on Algebraic Varieties

Emmanuel Peyre

ISBN 10: 3764366125 / ISBN 13: 9783764366124

Published by Springer, Basel, Birkhäuser Basel Okt 2001, 2001

About this Item

This item is printed on demand - it takes 3-4 days longer - Neuware -This book is devoted to the study of rational and integral points on higher dimensional algebraic varieties. It contains research papers addressing the arithmetic geometry of varieties which are not of general type, with an em phasis on how rational points are distributed with respect to the classical, Zariski and adelic topologies. The book gives a glimpse of the state of the art of this rapidly expanding domain in arithmetic geometry. The techniques involve explicit geometric con structions, ideas from the minimal model program in algebraic geometry as well as analytic number theory and harmonic analysis on adelic groups. In recent years there has been substantial progress in our understanding of the arithmetic of algebraic surfaces. Five papers are devoted to cubic surfaces: Basile and Fisher study the existence of rational points on certain diagonal cubics, Swinnerton-Dyer considers weak approximation and Broberg proves upper bounds on the number of rational points on the complement to lines on cubic surfaces. Peyre and Tschinkel compare numerical data with conjectures concerning asymptotics of rational points of bounded height on diagonal cubics of rank ~ 2. Kanevsky and Manin investigate the composition of points on cubic surfaces. Satge constructs rational curves on certain Kummer surfaces. Colliot-Thelene studies the Hasse principle for pencils of curves of genus 1. In an appendix to this paper Skorobogatov produces explicit examples of Enriques surfaces with a Zariski dense set of rational points. 446 pp. Englisch.

Seller Inventory # 9783764366124

Bibliographic Details

• Title: Rational Points on Algebraic Varieties
• Publisher: Springer, Basel, Birkhäuser Basel Okt 2001
• Publication Date: 2001
• Language: English
• ISBN 10: 3764366125
• ISBN 13: 9783764366124
• Binding: Buch
• Condition: Neu
• Dimensions: 23.5W x 15.5H x 0D centimeters 23.5 centimeters width by 15.5 centimeters height by 0 centimeters depth
• Weight: 830 grams

About this title

Synopsis

This book is devoted to the study of rational and integral points on higher­ dimensional algebraic varieties. It contains research papers addressing the arithmetic geometry of varieties which are not of general type, with an em­ phasis on how rational points are distributed with respect to the classical, Zariski and adelic topologies. The book gives a glimpse of the state of the art of this rapidly expanding domain in arithmetic geometry. The techniques involve explicit geometric con­ structions, ideas from the minimal model program in algebraic geometry as well as analytic number theory and harmonic analysis on adelic groups. In recent years there has been substantial progress in our understanding of the arithmetic of algebraic surfaces. Five papers are devoted to cubic surfaces: Basile and Fisher study the existence of rational points on certain diagonal cubics, Swinnerton-Dyer considers weak approximation and Broberg proves upper bounds on the number of rational points on the complement to lines on cubic surfaces. Peyre and Tschinkel compare numerical data with conjectures concerning asymptotics of rational points of bounded height on diagonal cubics of rank ~ 2. Kanevsky and Manin investigate the composition of points on cubic surfaces. Satge constructs rational curves on certain Kummer surfaces. Colliot-Thelene studies the Hasse principle for pencils of curves of genus 1. In an appendix to this paper Skorobogatov produces explicit examples of Enriques surfaces with a Zariski dense set of rational points.